This work conducts neural network modeling of temperature, thermal conductivity, and permeability predictions for depths greater than those drilled, as well as for the immediate vicinity of the exploratory borehole. For this purpose, we use data from three boreholes drilled earlier in the Soultz-sous-Forêts geothermal site (France) and the results of the magnetotelluric sounding performed there. It is shown that the relative accuracy of the predictions depends significantly on the relationship between the depth of the drilled borehole and the target depth of the prediction. For instance, for all the examined parameters, prediction errors become less than 5% if the prediction is made for depths that do not exceed the borehole depth by more than two times. In this case, the average errors of temperature and thermal conductivity predictions for the vicinity of the drilled borehole were 6%. The obtained results justified a new scheme for predicting the thermophysical and porosity/permeability properties of rocks while drilling exploratory geothermal boreholes.